Controlling the false discovery rate with dynamic adaptive procedures and of grouped hypotheses

dc.contributor.author

MacDonald, Peter William

dc.date.accessioned

2018-08-08 16:41:58 (GMT)

dc.date.available

2018-08-08 16:41:58 (GMT)

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2018-08-08

dc.date.submitted

2018-08-02

dc.identifier.uri

http://hdl.handle.net/10012/13549

dc.description.abstract

In the multiple testing problem with independent tests, the classical Benjamini-Hochberg (BH) procedure controls the false discovery rate (FDR) below the target FDR level.
Adaptive procedures can improve power by incorporating estimates of the proportion of true null hypotheses, which typically rely on a tuning parameter. Fixed adaptive procedures set their tuning parameters before seeing the data and can be shown to control the FDR in finite samples. In Chapter 2 of this thesis, we develop theoretical results for dynamic adaptive procedures whose tuning parameters are determined by the data. We show that, if the tuning parameter is chosen according to a left-to-right stopping time rule, the corresponding dynamic adaptive procedure controls the FDR in finite samples. Examples include the recently proposed right-boundary procedure and the widely used lowest-slope procedure, among others. Simulation results show that the right-boundary procedure is more powerful than other dynamic adaptive procedures under independence and mild dependence conditions.
The BH procedure implicitly assumes all hypotheses are exchangeable. When hypotheses come from known groups, this assumption is inefficient, and power can be improved through a ranking of significance that incorporates group information. In Chapter 3 of this thesis, we define a general sequential framework for multiple testing procedures in the grouped setting. We develop a flexible grouped mirrored knockoff (GMK) procedure which approximates the optimal ranking of significance. We show that the GMK procedure controls the FDR in finite samples, and give a particular data-driven implementation using the expectation-maximization algorithm. Simulation and a real data example demonstrate that the GMK procedure outperforms its competitors in terms of power and FDR control with independent tests.

en

dc.language.iso

en

en

dc.publisher

University of Waterloo

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dc.subject

simultaneous inference

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dc.subject

false discovery rate

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dc.subject

multiple hypothesis testing

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dc.subject

martingale

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dc.subject

stopping time

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dc.title

Controlling the false discovery rate with dynamic adaptive procedures and of grouped hypotheses

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dc.type

Master Thesis

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dc.pending

false

uws-etd.degree.department

Statistics and Actuarial Science

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uws-etd.degree.discipline

Statistics

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uws-etd.degree.grantor

University of Waterloo

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uws-etd.degree

Master of Mathematics

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The online abstract has been slightly altered to remove special math characters.